The work is devoted to the problems of manufacturing thinwalled parts of the aviation industry and instrument engineering on modern numerical control machines. The main reason of defects of such products -loss of dimensional accuracy is revealed. The reason for this is the elastic deformation of the workpiece during milling. A mathematical model for calculating the elastic pressing of a thin wall during milling is proposed. The method of checking the adequacy of the developed model with the help of engineering analysis system is presented. The minimum set of geometrical parameters of the processed element and the cutting tool necessary for search of the rational cutting mode was defined. A new approach to automation of this process present through the evaluation of all possible solutions. The calculation of the rational cutting mode was made taking into account the conditions of rigidity of the workpiece. Conclusions on the efficiency of the developed technique are made.